Let's abandon for a second the notion of strategically important, and just list human cognitive skills and modules, as they appear distributed in our cognition, according to the MIT The Cognitive Neurosciences (2009), and also as they come to mind while writing:

• Nurturing

• Lust

• Exploration

• Moral reasoning

• Agentism (animism, anthopomorphizing etc...)

• Language processing

• Proprioception

• Attachment

• Priming

• Allocating attention

• Simulation of future events

• Dreaming

• Empathizing

• Volition

• Consciousness

Now it's up to commenters to try and come up with reasons why these would be strategically important. Maybe they are, and then we'd have to verify if they are or not encompassed by the categories suggested by Bostrom. I don't have time to go through each in detail, but wanted to lay out a path for others who may find this useful.

Novel physics research, maybe. Just how useful that would be depends on just what our physics models are missing, and obviously we don't have very good bounds on that. The obvious application is as a boost to technology development, though in extreme cases it might be usable to manipulate physical reality without hardware designed for the purpose, or escape confinement.